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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

6. Surface Areas and Volumes of Spheres

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Exercise 13 Page 852

To find the area of a hemisphere, calculate the area of half of a sphere with the same radius and add the area of the great circle.

680.9in.^2

Practice makes perfect

A hemisphere is half of a sphere.

To find the area of a hemisphere we need to calculate the area of half of a sphere with the same radius and add the area of the great circle. Surface Area of a Hemisphere [0.8em] A=1/2(4π r^2)+π r^2 We first need to calculate the radius. To do so we will consider the given fact that the diameter is the radius two times. d=2r We can substitute 17 inches for d in this formula and solve for the radius r.

d=2r

d= 17

17=2r

.LHS /2.=.RHS /2.

8.5=r

Rearrange equation

r=8.5

We know that r=8.5inches. We can substitute this value into the formula for the area of a hemisphere and simplify.

A=1/2(4π r^2)+π r^2

r= 8.5

A=1/2(4π ( 8.5^2))+π ( 8.5^2)

▼

Evaluate right-hand side

Calculate power

A=1/2(4π (72.25))+π (72.25)

CommutativePropMult

Commutative Property of Multiplication

A=1/2(4(72.25)π )+72.25π

Multiply

A=1/2(289π )+72.25π

MoveRightFacToNumOne

1/b* a = a/b

A=289/2π+72.25π

Calculate quotient

A=144.5π+72.25π

Add terms

A=216.75π

Use a calculator

A=680.94...

Round to 1 decimal place(s)

A≈ 680.9

The area of the hemisphere to the nearest tenth is 680.9in^2.

Subchapter links

Exercises p.852-855